Study on overflow problem of numerical integration for layered elastic half-space systems

Abstract

Through a theoretical analysis for coefficients in the general expressions of stresses and displacements for a two-layer layered elastic half-space system (LEHS), the paper develops a modified method for these coefficients and new modified general expressions of stresses and displacements for LEHSs. The modified method is then applied to Love’s displacement function. The derived results show that the modified expressions of stresses and displacements for LEHSs no longer contain any positive exponential function. Theoretical derivation and numerical calculation suggest that the modified coefficients tend to zeroth, linear, or quadratic polynomial functions and that the positive exponential functions in the original general expressions of stresses and displacements for LEHSs, which result in numerical overflow, are just a balance to the quick vanishing of some coefficients. The modified method can reasonably avoid the overflow problem in the numerical integration for LEHSs. The numerical verification shows that the modified method is effective and reliable.